English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Expand the following:

(3a – 5b – c)² 

Expand the following:

(–x + 2y – 3z)²

Factorise the following:

9x² + 4y² + 16z² + 12xy – 16yz – 24xz

Factorise the following:

25x² + 16y² + 4z² – 40xy + 16yz – 20xz

Factorise the following:

16x² + 4y² + 9z² – 16xy – 12yz + 24xz

If a + b + c = 9 and ab + bc + ca = 26, find a² + b² + c².

Expand the following:

(3a – 2b)³ 

Expand the following:

`(1/x + y/3)^3`

Expand the following:

`(4 - 1/(3x))^3`

Find the following product:

`(x/2 + 2y)(x^2/4 - xy + 4y^2)`

Find the following product:

(x² – 1)(x⁴ + x² + 1)

Without actually calculating the cubes, find the value of:

`(1/2)^3 + (1/3)^3 - (5/6)^3`

Without actually calculating the cubes, find the value of:

(0.2)³ – (0.3)³ + (0.1)³

Find the value of x³ + y³ – 12xy + 64, when x + y = – 4

Find the value of x³ – 8y³ – 36xy – 216, when x = 2y + 6

Give possible expressions for the length and breadth of the rectangle whose area is given by 4a² + 4a – 3.

Simplify (2x – 5y)³ – (2x + 5y)³.

Multiply x² + 4y² + z² + 2xy + xz – 2yz by (–z + x – 2y).

If a + b + c = 5 and ab + bc + ca = 10, then prove that a³ + b³ + c³ – 3abc = – 25.

Prove that (a + b + c)³ – a³ – b³ – c³ = 3(a + b)(b + c)(c + a).